In 900
900 = 2^{2}×3^{2}×5^{2}.
(A) Number of factors(divisors) are possible?
(2+1) * (2+1) * (2+1) = 27
(B) Number of Even factors are possible?
you need even divisor means you must included '2' and any no multiply with the 2 given even number
(2)*(2+1)*(2+1) = 18
(C) Number of Odd-factors are possible?
"didn't include '2' "
(2+1)*(2+1) = 9
(D) If the number is divisible by 25 then a number of factors are possible?
25 = 5^{ 2}
Number must have the multiple of 5^{2} then only it's divisible by 25 right ??
(2+1)*(2+1)*(1) = 9
(E) Sum of factors?
= (2^{ 0 }+ 2^{1 }+ 2^{2}) x (3 ^{0} + 3^{1} + 3 ^{2}) x (5 ^{0 }+ 5 ^{1 }+ 5 ^{2})
= $(\frac{2^{3}-1}{2-1}) X (\frac{3^{3}-1}{3-1}) X( \frac{5^{3}-1}{5-1})$
F) Product of factors = (Number)^{ no of factors /2}
^{ }= (900) ^{27/2}